Transverse plane

About: Transverse plane is a research topic. Over the lifetime, 17069 publications have been published within this topic receiving 194059 citations. The topic is also known as: axial plane.

Apparatus for locating transverse holes of intramedullary implantates

Abstract: The apparatus serves to locate transverse holes V of intramedullary implantates, especially in the distal end of implanted interlocking nails, in the fracture treatment of bones. The apparatus includes at least one magnet (13, 16) generating an axially symmetrical field, and a magnetic field detection device (8, 9) having an axial reception characteristic, with one of said two directional elements being adapted to be aligned on the axis of the transverse hole (11) to be located. The other one of said two directional elements, e.g. the magnet (13), is freely movable exteriorly, and therefore adapted to be aligned with the axis of the transverse hole. The output signals of the magnetic field detection device (8, 9) are presented on a display device (17) through a signal processing device (15). By relative displacement of the magnet (13) and of the magnetic field detection device (8, 9), the two axes thereof may be made to coincide, which state can be displayed on the display device by a zero point indication.

Cooperative frequency locking and stationary spatial structures in lasers

Abstract: We investigate the spontaneous emergence of transverse patterns in lasers by using both the standard two-level model and the so-called cubic approximation, which is generally valid in the threshold regions. The stationary intensity configurations fall into two distinct classes. The first includes solutions of the single-mode type with the frequency and spatial structure of one of the transverse resonances. The solutions of the second group involve the simultaneous oscillation of several cavity modes, operating in such a way as to produce a stationary intensity profile. The stationary character of these multimode configurations emerges from the fact that the transverse modes of the resonator lock onto a common frequency during the nonlinear transient. We call this phenomenon cooperative frequency locking.

Two-dimensional spreading of a granular avalanche down an inclined plane Part I. theory

Abstract: This paper is concerned with the motion of an unconfined finite mass of a granular material released from rest on an inclined plane. The granular mass is treated as a frictional Coulomb-like continuum with a Coulomb-like basal friction law. Depth averaged equations are deduced from the three-dimensional dynamical equations by scaling the equations and imposing the shallowness assumption that the moving piles are long and wide but not deep. Several distinguished limits for small depth to length and depth to width ratios can be analysed. We develop an approximate theory based upon the full dynamical equations parallel to the inclined plane and imposed hydrostatic pressure conditions perpendicular to it. The resulting model equations are then applied to construct either yet simpler model equations or else solutions for particular cases. In a first application the transverse distributions of the velocity fields and of the depth profile are prescribed, while representative values of these functions (such as the cross sectional averages or maxima) as functions of time and the downhill coordinate are left unspecified. For these quantities evolution equations are obtained from a lateral averaging of the vertically averaged equations. In a second application approximate similarity solutions of the spatially two-dimensional equations are derived. The depth and velocity profiles for the moving mass are determined in analytical form, and the evolution equation for the total length and the total width of the pile is integrated numerically. A parameter study illustrates the performance of the model.

Stability of Transverse Shear Flows in Shallow Open Channels

Abstract: The bed-friction effect on the stability of transverse shear flows in shallow open channels is examined using a linear and “inviscid” theory. Numerical calculations are conducted for four groups of parallel flows with inflection-point velocity profiles. The necessary conditions for the transverse shear flows to become unstable, so that the large-scale transverse motion may coexist with the small-scale bed-generated turbulence, are determined from the calculations. The results are correlated with two dimensionless parameters: a bed-friction number and an ambient-velocity parameter. The bed-friction number quantifies the stabilizing effect of the bed-friction. The ambient-velocity parameter characterizes the changes in depth and roughness across the open-channel flows. In the limiting case of a weak transverse shear flow, when the change in velocity across the flow is small, the bed-friction number becomes the only dimensionless parameter governing the stability of the transverse shear flows. The critical values of this bed-friction number for the weak transverse shear flows with hyperbolic-tangent and hyperbolic-secant velocity profiles, are 0.120 and 0.145, respectively.